[R-sig-ME] Testing overdispersion Gamma glmer
Highland Statistics Ltd
highstat at highstat.com
Mon Dec 14 12:16:27 CET 2015
------------------------------
Message: 2
Date: Mon, 14 Dec 2015 11:45:24 +0100
From: Sophie Waegebaert <sophie.waegebaert at gmail.com>
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] Testing overdispersion Gamma glmer
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<CAGH66HCiv5jiad+_DM+HP91xP3GOHGa1jft8E=KYSJR=i_RYmQ at mail.gmail.com>
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Hello,
I want to compare mean trip duration (length.in.hours) across treatment
conditions and colonies. I have 3 colonies and 2 treatments. So, one half
of a colony gets a DWV treatment and the other half a control treatment.
When a histogram is made, it is clear that the data is skewed to the rigth.
So, I am using a Gamma distribution.
This is the model: fit_length = glmer(length.in.hours~treatment*colony +
(1|RFID), family = Gamma(link = "log"), data = datashort)
I use the log link and not the identity link, because the AIC is lower.
RFID is the code used for each subject in the colonies.
I want to test for the overdispersion assumption by using the following
code:
> datashort$obs = factor(1:nrow(datashort))> fit_length_obs = glmer(length.in.hours~treatment*colony + (1|RFID) + (1|obs), family = Gamma(link = "log"), data = datashort)
> AIC(fit_length, fit_length_obs) df AIC
fit_length 8 5646.758
fit_length_obs 9 -74390.105
There is a clear difference between the AIC values, but I was wondering
wether -74390 is a realistic value? Is it not very low? Or am I using the
wrong method to control for overdispersion?
Thank you for some help!
Kind regards,
Sophie
Sophie,
A Gamma GLM(M) cannot be overdispersed. The parameter r in the variance expression of a Gamma GLM acts
like the sigma parameter in linear regression.
A Poisson GLM can be overdispersed because the variance equals the mean. It has no extra parameter to correct for any
extra variation. Same holds for a binomial (as in binomial..not Bernoulli).
As to why the model with the observation level random effect is much better...well it acts like
a latent variable.
Kind regards,
Alain
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